Special Year 2020-21: Virtual Workshop on Representation Theory and Geometry

Abstract: In 2000, Arnaud Beauville introduced the notion of symplectic singularities and raised the question of classifying isolated symplectic singularities with trivial local fundamental group: the latter condition is meant to avoid the numerous...

In 1997, Kuperberg gave a generators-and-relations presentation of the monoidal category Fund, whose objects are tensor products of fundamental representations, for all rank 2 lie algebras. The general case has been an open problem since. It was...

The talk is based on a joint work with Pablo Boixeda Alvarez. We study equivariant Borel-Moore homology of certain affine Springer fibers and relate them to global sections of suitable vector bundles arising from Procesi bundles on Q-factorial...

The study of totally positive matrices, i.e., matrices with positive minors, dates back to 1930s. The theory was generalised by Lusztig to arbitrary split reductive groups using canonical bases, and has significant impacts on the theory of cluster...

Let G be a semisimple group over an algebraically closed field of large characteristic. There are two important types of rational representations of G: the Weyl modules and the simple modules. We will explain how to go from the first type to the...

A symplectic singularity has a natural stratification by Poisson leaves, which are symplectic, hence even-dimensional.  Perverse sheaves constructible with respect to this stratification are semisimple if the coefficients are in characteristic zero...

According to Langlands’ conjectures, algebraic automorphic forms should be parametrized by global Galois representations, and smooth representations of $p$-adic groups should be parametrized by local Galois representations. These parametrizations...

I will describe a program aimed at understanding numerics of representations of quantized symplectic resolutions in positive characteristic. A key ingredient is a generalization of the action of the affine braid group on the derived category of...

The workshop was organized by Geordie Williamson(IAS/University of Sydney) and took place virtually.

Geometric representation theory has proved itself to be an unreasonably effective tool in pure mathematics. This conference (the...